$[6$ pts$]$ A heat pump has a COP of $2\mathrm{.}6,$ and operates between a high

temperature space at $480R$ and a low temperature space at $400R.$

a$.$ To provide $12,000Bt\frac{u}{h}r$ to the warm space, what is the rate of work $($in

kW$)$ required?

b$.$ What is the rate of heat transfer from the cool space?

c$.$ If the heat pump was reversible, for the same temperature difference,

what would its COP be$?$